"""
Copyright 2021 The CVXPY Developers

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""


import warnings

import numpy as np
import scipy  # For version checks

import cvxpy.settings as s
from cvxpy.constraints import NonNeg, Zero
from cvxpy.reductions.solution import Solution, failure_solution
from cvxpy.reductions.solvers import utilities
from cvxpy.reductions.solvers.conic_solvers.conic_solver import ConicSolver
from cvxpy.utilities.versioning import Version


class SCIPY(ConicSolver):
    """An interface for the SciPy linprog function.
    Note: This requires a version of SciPy which is >= 1.6.1
    """
    SUPPORTED_CONSTRAINTS = ConicSolver.SUPPORTED_CONSTRAINTS

    # Solver capabilities.
    if (Version(scipy.__version__) < Version('1.9.0')):
        MIP_CAPABLE = False
    else:
        MIP_CAPABLE = True
        MI_SUPPORTED_CONSTRAINTS = SUPPORTED_CONSTRAINTS

    # Map of SciPy linprog status
    STATUS_MAP = {0: s.OPTIMAL,  # Optimal
                  1: s.OPTIMAL_INACCURATE,  # Iteration/time limit reached
                  2: s.INFEASIBLE,  # Infeasible
                  3: s.UNBOUNDED,  # Unbounded
                  4: s.SOLVER_ERROR  # Numerical difficulties encountered
                  }

    def import_solver(self) -> None:
        """Imports the solver.
        """
        from scipy import optimize as opt  # noqa F401

    def name(self):
        """The name of the solver.
        """
        return s.SCIPY

    def apply(self, problem):
        """Returns a new problem and data for inverting the new solution.

        Returns
        -------
        tuple
            (dict of arguments needed for the solver, inverse data)
        """
        data = {}
        inv_data = {self.VAR_ID: problem.x.id}

        if not problem.formatted:
            problem = self.format_constraints(problem, None)
        data[s.PARAM_PROB] = problem
        data[self.DIMS] = problem.cone_dims
        inv_data[self.DIMS] = problem.cone_dims

        variables = problem.x
        data[s.BOOL_IDX] = [int(t[0]) for t in variables.boolean_idx]
        data[s.INT_IDX] = [int(t[0]) for t in variables.integer_idx]
        inv_data['is_mip'] = data[s.BOOL_IDX] or data[s.INT_IDX]

        constr_map = problem.constr_map
        inv_data[self.EQ_CONSTR] = constr_map[Zero]
        inv_data[self.NEQ_CONSTR] = constr_map[NonNeg]
        len_eq = problem.cone_dims.zero

        c, d, A, b = problem.apply_parameters()
        data[s.C] = c
        inv_data[s.OFFSET] = d
        data[s.A] = -A[:len_eq]
        if data[s.A].shape[0] == 0:
            data[s.A] = None
        data[s.B] = b[:len_eq].flatten()
        if data[s.B].shape[0] == 0:
            data[s.B] = None
        data[s.G] = -A[len_eq:]
        if 0 in data[s.G].shape:
            data[s.G] = None
        data[s.H] = b[len_eq:].flatten()
        if 0 in data[s.H].shape:
            data[s.H] = None
        return data, inv_data

    def solve_via_data(self, data, warm_start: bool, verbose: bool, solver_opts, solver_cache=None):
        from scipy import optimize as opt

        # Set default method which can be overriden by user inputs
        if (Version(scipy.__version__) < Version('1.6.1')):
            meth = "interior-point"
        else:
            meth = "highs"

        # Check if the problem is a MIP.
        problem_is_a_mip = data[s.BOOL_IDX] or data[s.INT_IDX]

        # Track variable integrality options. An entry of zero implies that
        # the variable is continuous. An entry of one implies that the
        # variable is either binary or an integer with bounds.
        if problem_is_a_mip:
            integrality = [0] * data[s.C].shape[0]

            for index in data[s.BOOL_IDX] + data[s.INT_IDX]:
                integrality[index] = 1

            bounds = [(None, None)] * data[s.C].shape[0]

            for index in data[s.BOOL_IDX]:
                bounds[index] = (0, 1)
        else:
            integrality = None
            bounds = (None, None)

        # Extract solver options which are not part of the options dictionary
        if solver_opts:

            # Raise error message if the parameters are not passed in
            # a dictionary called 'scipy_options'.
            if "scipy_options" not in solver_opts:
                raise ValueError("All parameters for the SCIPY solver should "
                                 "be encased within a dictionary called "
                                 "scipy_options e.g. \n"
                                 "prob.solve(solver='SCIPY', verbose=True,"
                                 " scipy_options={'method':'highs-ds', 'maxiter':10000})")

            if Version(scipy.__version__) < Version('1.9.0'):
                # Raise warning if the 'method' parameter is not specified
                if "method" not in solver_opts['scipy_options']:
                    self._log_scipy_method_warning(meth)

            if "method" in solver_opts["scipy_options"]:
                meth = solver_opts["scipy_options"].pop("method")

                # Check to see if scipy version larger than 1.6.1 is installed
                # if method chosen is one of the highs methods.
                ver = (Version(scipy.__version__) < Version('1.6.1'))
                if ((meth in ['highs-ds', 'highs-ipm', 'highs']) & ver):
                    raise ValueError("The HiGHS solvers require a SciPy version >= 1.6.1")

            # Disable the 'bounds' parameter to avoid problems with
            # canonicalised problems.
            if "bounds" in solver_opts['scipy_options']:
                raise ValueError("Please do not specify bounds through "
                                 "scipy_options. Please specify bounds "
                                 "through CVXPY.")

            # Check that the 'integrality' parameter isn't specified.
            if "integrality" in solver_opts['scipy_options']:
                raise ValueError("Please do not specify variable integrality through "
                                 "scipy_options. Please specify variable types "
                                 "through CVXPY.")

            # Check for SciPy method support (i.e., only 'highs' supports MIP models).
            method_supports_mip = meth == 'highs'

            if problem_is_a_mip and not method_supports_mip:
                raise ValueError("Only the 'highs' SciPy method can solve MIP models.")

            # Not supported by HiGHS solvers:
            # callback = solver_opts['scipy_options'].pop("callback", None)
            # x0 = solver_opts['scipy_options'].pop("x0", None)
        else:
            # Instantiate an empty `scipy_options` entry.
            solver_opts['scipy_options'] = {}

            if Version(scipy.__version__) < Version('1.9.0'):
                self._log_scipy_method_warning(meth)

        if problem_is_a_mip:
            constraints = []
            G = data[s.G]
            if G is not None:
                ineq = scipy.optimize.LinearConstraint(G, ub=data[s.H])
                constraints.append(ineq)
            A = data[s.A]
            if A is not None:
                eq = scipy.optimize.LinearConstraint(A,data[s.B], data[s.B])
                constraints.append(eq)
            lb = [t[0] if t[0] is not None else -np.inf for t in bounds]
            ub = [t[1] if t[1] is not None else np.inf for t in bounds]
            bounds = scipy.optimize.Bounds(lb, ub)
            solution = opt.milp(data[s.C], 
                                constraints=constraints,
                                options=solver_opts['scipy_options'],
                                integrality=integrality,
                                bounds=bounds)
        else:
            solution = opt.linprog(data[s.C], A_ub=data[s.G], b_ub=data[s.H],
                                   A_eq=data[s.A], b_eq=data[s.B], method=meth,
                                   options=solver_opts['scipy_options'],
                                   bounds=bounds)

        # Replace `scipy_options` method to avoid future warnings.
        solver_opts["scipy_options"]["method"] = meth

        if verbose is True:
            print("Solver terminated with message: " + solution.message)

        return solution

    def _log_scipy_method_warning(self, meth):
        warnings.warn("It is best to specify the 'method' parameter "
                      "within scipy_options. The main advantage "
                      "of this solver is its ability to use the "
                      "HiGHS LP solvers via scipy.optimize.linprog(), "
                      "which requires a SciPy version >= 1.6.1."
                      "\n\nThe default method '{}' will be"
                      " used in this case.\n".format(meth))

    def invert(self, solution, inverse_data):
        """Returns the solution to the original problem given the inverse_data.
        """
        status = self.STATUS_MAP[solution["status"]]

        # Sometimes when the solver's time limit is reached, the solver doesn't return a solution.
        # In these situations we correct the status from s.OPTIMAL_INACCURATE to s.SOLVER_ERROR
        if (status == s.OPTIMAL_INACCURATE) and (solution.x is None):
            status = s.SOLVER_ERROR

        primal_vars = None
        dual_vars = None
        if status in s.SOLUTION_PRESENT:
            primal_val = solution['fun']
            opt_val = primal_val + inverse_data[s.OFFSET]
            primal_vars = {inverse_data[self.VAR_ID]: solution['x']}

            # SciPy linprog only returns duals for version >= 1.7.0
            # and method is one of 'highs', 'highs-ds' or 'highs-ipm'
            # MIP problems don't have duals and thus are not updated.
            if 'ineqlin' in solution and not inverse_data['is_mip']:
                eq_dual = utilities.get_dual_values(
                    -solution['eqlin']['marginals'],
                    utilities.extract_dual_value,
                    inverse_data[self.EQ_CONSTR])
                leq_dual = utilities.get_dual_values(
                    -solution['ineqlin']['marginals'],
                    utilities.extract_dual_value,
                    inverse_data[self.NEQ_CONSTR])
                eq_dual.update(leq_dual)
                dual_vars = eq_dual
            
            attr = {}
            if "nit" in solution: # Number of interior-point or simplex iterations
                attr[s.NUM_ITERS] = solution['nit']
            if "mip_gap" in solution: # Branch and bound statistics
                attr[s.EXTRA_STATS] = {"mip_gap": solution['mip_gap'], 
                                       "mip_node_count": solution['mip_node_count'], 
                                       "mip_dual_bound": solution['mip_dual_bound']}

            return Solution(status, opt_val, primal_vars, dual_vars, attr)
        else:
            return failure_solution(status)
